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Simplifying (x + 0.6)(x + 1.1) = 0 Reorder the terms: (0.6 + x)(x + 1.1) = 0 Reorder the terms: (0.6 + x)(1.1 + x) = 0 Multiply (0.6 + x) * (1.1 + x) (0.6(1.1 + x) + x(1.1 + x)) = 0 ((1.1 * 0.6 + x * 0.6) + x(1.1 + x)) = 0 ((0.66 + 0.6x) + x(1.1 + x)) = 0 (0.66 + 0.6x + (1.1 * x + x * x)) = 0 (0.66 + 0.6x + (1.1x + x2)) = 0 Combine like terms: 0.6x + 1.1x = 1.7x (0.66 + 1.7x + x2) = 0 Solving 0.66 + 1.7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.66' to each side of the equation. 0.66 + 1.7x + -0.66 + x2 = 0 + -0.66 Reorder the terms: 0.66 + -0.66 + 1.7x + x2 = 0 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 0.00 + 1.7x + x2 = 0 + -0.66 1.7x + x2 = 0 + -0.66 Combine like terms: 0 + -0.66 = -0.66 1.7x + x2 = -0.66 The x term is 1.7x. Take half its coefficient (0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. 1.7x + 0.7225 + x2 = -0.66 + 0.7225 Reorder the terms: 0.7225 + 1.7x + x2 = -0.66 + 0.7225 Combine like terms: -0.66 + 0.7225 = 0.0625 0.7225 + 1.7x + x2 = 0.0625 Factor a perfect square on the left side: (x + 0.85)(x + 0.85) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + 0.85) equal to 0.25 and -0.25.Subproblem 1
x + 0.85 = 0.25 Simplifying x + 0.85 = 0.25 Reorder the terms: 0.85 + x = 0.25 Solving 0.85 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = 0.25 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = 0.25 + -0.85 x = 0.25 + -0.85 Combine like terms: 0.25 + -0.85 = -0.6 x = -0.6 Simplifying x = -0.6Subproblem 2
x + 0.85 = -0.25 Simplifying x + 0.85 = -0.25 Reorder the terms: 0.85 + x = -0.25 Solving 0.85 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = -0.25 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = -0.25 + -0.85 x = -0.25 + -0.85 Combine like terms: -0.25 + -0.85 = -1.1 x = -1.1 Simplifying x = -1.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.6, -1.1}
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